Normal forms, symmetry and linearization of dynamical systems

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, , Citation Dario Bambusi et al 1998 J. Phys. A: Math. Gen. 31 5065 DOI 10.1088/0305-4470/31/22/009

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1 Dipartimento di Matematica, Università di Milano, via Saldini 50, 20133 Milano, Italy

2 Dipartimento di Fisica, Università di Pisa, Piazza Torricelli 2, 56126 Pisa, Italy

3 Department of Mathematics, Loughborough University, Loughborough LE11 3TU, UK

4 Dipartimento di Scienze Fisiche, Università di Napoli, and INFN, Sezione di Napoli, Mostra d'Oltremare, 80123 Napoli, Italy

Dates

  1. Received 3 July 1997

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Abstract

We discuss how the presence of a suitable symmetry can guarantee the perturbative linearizability of a dynamical system - or a parameter-dependent family - via the Poincaré normal form approach. We discuss this formally at first, and later pay attention to the convergence of the linearizing procedure. We also discuss some generalizations of our main result.

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